What is the difference between “free” software and “open source” software?

The source code of open source software is “open”, you can have a look at it. In contrast to "closed source". Because, usually, you do not have the source code of closed software: it is distributed as compiled executable files (file.exe) only. Examples are Microsoft products, Adobe Photoshop etc.

Free” software goes beyond “open” software. For free software, you have the right not only to have a look at the source code. You can also change it.
If you want to know whether a software is free or open, please see the license text. For example, "gpl", "lgpl" or the "apache license" are "free". Formerly, “open software” contained the idea of “free software”. But now this distinction between both ideas are made.

See  more details on this topic in the training material section, Block1-Statements about FLOSS.pdf (405Ko), Block4-Open Source Licences.pdf (276Ko) and  Block5-FLOSS Licences Details.pdf (294Ko).

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