Engagement Types are setup at the Company level in Settings > Lists > Engagement Types.

Engagements are the type of services your firm offers.  Examples for a CPA firm could be as follow:

Accounting
Payroll
Tax
Audit
Consulting

A Law Firm could have Engagement Types as follows:

Litigation
Consulting
Contracts
Domestic Cases

An Engagement type of Tax would be a broad Engagement category that could include all types of tax returns your firm may prepare for clients.  In this scenario, at the client level, it is possible to create an Engagement Type - Tax for a Client and name the engagement, at the client level, Form 1040.  The description is only used to identify the engagement and can be named anything.  But for reporting, it will be grouped by the Engagement Type - Tax.  This type of Engagement is very broad, but if segmenting the Engagement types is of no concern then this is a possible scenario.

If you want more segmentation then it is recommended to setup each type of tax return as an Engagement Type at the Company level.   The following could be Engagements Types:

1040
1120
1120S
990
1065

For Reporting purposes the Engagement types would now be segmented by the type of tax return.   It all depends on how much detail and segmentation is required for reporting purposes.

All clients are required to have engagements for invoicing regardless if time tracking is utilized.

Creating an Engagement for a client is as simple as selecting the Engagement Type from the drop-down list (Engagement Types that were setup at the Company Level) and then either using the default Engagement Name or changing it.  

Important:  Engagements can have 2 different Billing Methods, Hourly or Fixed Fee.  

When Invoicing a client, if Hourly is the chosen method, then the total of all time records will be used as the Invoice Amount by default.  This amount can be changed at the invoice level.

When Invoicing a client, if Fixed Fee is the chosen method, then the fixed fee amount will be used for the invoice amount and the write/up down will automatically be calculated.  This amount can be changed at the invoice level.

If a default invoice description is entered, this description will automatically be populated for the invoice line items and the invoice memo.  The default invoice descriptions can be modified during invoice.  It is important to note that having a default description speeds up the invoicing process tremendously!

Engagements allow Activities to be grouped by Engagement.  What does this mean?

Some sample work Activities could be as follows:
Meeting
Telephone Call
Bookkeeping
Tax Preparation
Document Preparation
Payroll Processing
Quarterly Reports
Yearly Reports

Since every business typically provides multiple types of services (Engagements) the Activities can be grouped to a specific Client Engagement.  Example:

Client - ABC has 3 Engagements
Payroll
Form 1040
Accounting

When tracking time the following are some possible scenarios:

ABC - Payroll (Engagement)
  Meeting
  Telephone Call
  Processing Payroll
  Quarterly Reports
  Yearly Reports

ABC - Accounting (Engagement)
  Meeting
  Telephone Call
  Bookkeeping

ABC - Form 1040
  Meeting
  Tax Preparation
  Assembly

As you can see, with Engagement based billing, Activities can be grouped to the Engagement for which you are working on.  The Meeting Activity can be used for any Engagement.  Notice the Payroll Engagement. Different Activities can be grouped to an Engagement.  For reporting purposes and billing purposes, this is a streamlined approach for knowing which Activities were provided for which Engagement.

When invoicing, all Engagements with Open Time, will be displayed for billing purposes.  Based on invoiced amounts, the write/up down amounts will automatically be calculated.

If time tracking is not utilized then during the Invoicing process, simply select the Client's Engagement from the drop-down and enter an amount to invoice.  Based on invoiced amounts, the write/up down amounts will automatically be 100% write-up.

Once a client is selected, that client's Engagements will be populated in the drop-down list.  Select the Engagement for which your time record covers and then select the Activity.

FAQ's

>Is there a way to mass delete an engagement from clients?

you can delete engagements from clients if they do not have unbilled time or invoice history. General Settings > Utilities > Delete Active/Inactive Engagements

>So when you assign an engagement to a client and assign to someone they become the manager. Can you someone explain what this means?

Because the system indicates they are the manager of that engagement once assigned.

It just shows who the logged in user was that assigned the engagement. that is all. It has no effect on anything.

>a customer that has made an engagement inactive however their staff still sees this as an option within the Time Entry screen

If Engagement is selected as Close at the client level. It does not show in Time Entry for the Client. This is controlled in client>Engagement>Status

Making engagements inactive at the firm level does not control engagements at the client level. Inactive engagements at the firm level, will ensure that the engagement will not be available to add to clients.

>If I select a client to input time on will it only show individual engagement codes or activity codes

Engagements are unique to the client, only the ones assigned to that client will show in drop down.
Activity codes are set at company level so all of those will show.

>I have created duplicate engagements and need to get rid of the duplicates

That can be done in Settings>Lists>Engagement Types. Use the trash can to delete the duplicates. You will not be able to delete the engagements if they are time records associated with them. You may reassign the time records to another engagement, if you would like.

>I am trying to find out why we have a duplicate engagement under a client and how I can get rid of it.

You can remove the duplicate engagement from the client by going into the client profile, navigating to the engagements tab and then using the delete (trash can icon) directly to the right of the engagement name.

>how to transfer time from one engagement to another when you have a duplicate engagement or you have time associated with the wrong engagement

So you will need to go into the Time & Expense tab within that Client Profile. From there, click on the red pencil icon to the left of the DNU - NonBillable row. From there, make sure all time records are selected and click the Batch Options drop down from the upper right hand corner. From that drop down you will select Reassign Selected Items. From there select the correct Engagement (NonBillable) from the Engagement drop down and click Reassign. Once these time entries are reassigned to the correct engagement you should then be able to delete the DNU - NonBillable engagement from the engagements tab within the Client Profile.

>is there a way to mass delete client's engagements?

There is no way to mass delete the engagements. There is a way to delete engagements and, that may be done in settings> lists> engagements types. And, you may use the red trash can icon to delete them. You will not be able to delete the engagements if they are time records associated with them. You may reassign the time records to another engagement, if you would like.

>Is there a way to only assign certain activities to certain engagements as I don't want all engagements to be tied to all activities?

no there is no way to limit activities to engagement in the current Mango