It gets "obvious" *after* the first time you work it out.
A relay is a push-button switch(es) and an electromagnet to "push the button".
The drawings are somewhat conventionalized for drawing simplicity; most relay users know the convention.
In relays and in switches, what Shooter said: "NO" is Normally Open; "NC" is Normally Closed, where "Normal" is no push/coil-current.
A plain house door-bell button is Normally Open. No push, no path from battery to bell, no ring.
A home furnace has a 24V (for safety) thermostat switch and a 24V relay at the furnace. If it is warm-enough (or the thermostat wires break), the NO function ensures the furnace does not run.
My car has a headlight high/low relay. Normally headlight power (from yet another relay!) flows through the NC contacts to the Low beam lights. When I click the thingie, the hi/lo relay coil is energized and now the NC contacts open, the NO contacts close, the High beams come on and the low beams go off.
You can re-verify these thoughts with a continuity checker for the contacts and an appropriate battery for the coil.
I would not say a diode is "typical". Many/most relays do not have one. But a lot of 5VDC relays do, because they are typically run from logic chips, which need the protection, and an on-board diode saves a penny in assembly. Check for this and be sure you get it right way round!