What are 'threads' and 'memory' (MB) at the analysis board?

What are 'threads' and 'memory' (MB) at the analysis board?
And what are the recomended settings? If I chose more memory (MB) will other tings on the computer run slower?

These are resources available for the engine to run. In general, more threads and more memory should allow the engine to run faster (or get deeper in the same time). But there are some limits, e.g. the number of threads should not exceed the number of your logical CPUs (cores). In other words, on a 12-core CPU setting to more than 12 threads should not help any more (and often you would rather like to go 1-2 lower to avoid competing with your desktop environment and browser. In theory, you might try to go up to the double of the number of your cores if your CPU supports hyperthreading but in my experience it does not really help. As for memory, giving too much of it may result in engine crashing or exhausting available memory; but on a reasonably new desktop system you should be perfectly fine even with the maximum.

Here is official Stockfish FAQ that may be useful if you are running Stockfish on your own machine. https://github.com/official-stockfish/Stockfish/wiki/Stockfish-FAQ. Here are recommendations for Komodo engines https://komodochess.com/store/pages.php?cmsid=14. If you are using other engines, you should look at the respective homepages where you may find recommendations. But the above pages for Stockfish and Komodo should give you a good general idea.