The basic meaning of「厚」is thick, large, deep, strong. I also found the meaning kind, cordial. However I wonder why it is at the beginning of the compound「厚生労働省」.
As a prior answer points out, 厚生 means "welfare". I'd like to add some sources to that, because I can see where you may have been stuck: how is "thick" related to "welfare", right?
If you see the bolded part, the kanji 厚 here brings in the idea of to add/increase, and to make stronger. That's where the sense of "welfare" and "better quality of life" comes in.
This can be further adumbrated by this definition found on Wiktionary, the key words 豊か, 増進する:
Note that the adjective 厚い is related to this usage:
abundant (Only applies to 厚い)