Indexing will not slow down your SSD. However, most SSD's are so fast that indexing is not really required. Indexing also has the potential of increasing read/writes on SSD's and over time can affect (very, very slightly) SSD life. Make either choice, it will not have any impact on your SSD speed.
If you have that setting checked then you can search on the contents of (for example) Word or Excel files. So you can search for all files containing a specific word.
If you don't have it checked then you can only search on the names of files.
It will not slow things down much - I have it checked (as it is by default). You can also specify by file type whether to index file contents - by default .txt and .pdf have contents indexed but .jpg and .exe do not for example. This is set in the advanced tab of Indexing Options.