I tested this on CentOS 7 with Mate 1.16.2, but it should work similarly on Ubuntu.
Enabling snapping by dragging windows with your mouse:
Open the "Windows" control panel under System - Preferences - Look and Feel - Windows. Go to the tab "Placement" and check Enable side by side tiling.
Enabling snapping with keyboard shortcuts:
Open the "Keyboard Shortcuts" control panel under System - Preferences - Hardware - Keyboard Shortcuts. Assign the following keys (although there might be more of interest, depends on your personal preferences). I'm using the keybinds I'm familiar with from Windows 7/10 here, which uses the "Windows" key in combination with an arrow key (instead of Super the configuration screen might show Mod4 or similar):
Maximize Window - Super+Up
Restore Window - Super+Down
Tile window to the east (right) side of the screen - Super+Right
Tile window to the west (left) side of the screen - Super+Left