Spacemacs uses evil-mode which is a VI emulation layer. Evil-mode adds VI modal editing to spacemacs. In a nutshell modal editing has different modes where keybindings do different things. This is partly so that keybindings can remain short and easy to remember.
In essence, the answer to your question is that you enter the space character by switching to ...
Use C-s (company-search-candidates), use C-h f company-search-candidates to learn more:
company-search-candidates is an interactive compiled Lisp function in
Start searching the completion candidates incrementally.
Search can be controlled with the commands: