On Ubuntu/Debian these can be installed by invoking
sudo apt-get install libboost-filesystem-dev libboost-system-dev
On macOS Boost is available through the Homebrew package manager, it might be advisable to use a Homebrew installed Python for installing pyhector:
brew install boost
Windows is (as Hector) in principle supported but not yet tested for pyhector. Pull request with installation notes for Windows are welcome.