You'll notice that notes on staff paper have "stems" — lines that "come off" their bodies.
If the notes are high up on the staff paper, the stem comes down.
If the notes are low on the staff paper, the stem comes up.
Stems help clue you into the "time value" of notes, as you can see here.
For all notes that are "quicker" than 1/4 notes (such as 1/8th and 1/16th notes), "beams" are used to connect the stems together.
Their purpose is probably for readability. These "quicker" notes are usually more condensed on the page, so the beams help in skimming the music.
If 1/8th notes or 1/16th notes or 1/32nd notes are written individually, they're written with tails (or "flags") instead.
Group 1: the single tail / single beam - 1/8th notes
Group 2: the double tail / double beam - 1/16th notes
Group 3: the triple tail / triple beam - 1/32nd notes