I'm currently working with a new team who haven't really worked in an Agile way before, nor do they have much experience of what types of testing you can do on an application, so in preparation I tried to come up with simple definitions on the above types of tests.
I thought it would make a good blog post, as it's somethign that I would undoubtedly find useful at a future point... So here goes:
To define a Unit Test it's a simple test that tests a single piece of code/logic. When it fails it will tell you what piece of code is broken.
An Integration Test is a test that tests the combination of different pieces of an application, when it fails it will tell you that your system(s) are not working together as you thought they would.
An Acceptance Test is a test that tests the software does what is expected by the customer/user of the software. When it fails it tells you that your application is not doing what the customer/user thought it would do or even what it should do.
These are quick, simple and dirty definitions of the different types of testing you might come across in a project, there are more, but these are the ones that I am going through with the team, so these are the ones that have made it into this blog post!
Feel free to agree/disagree/add more...