Every altimeter is just a pressure gauge wearing a height costume. For it to mean anything, everyone nearby has to agree on the reference — and the transition system is that agreement, written into the climb and descent of every flight.
Three terms, one picture
The transition altitude belongs to the climb: it's the altitude at which you reset the subscale from local QNH to the standard setting of 1013.25 hPa. From that moment you're flying flight levels, not altitudes. The transition level belongs to the descent — the level at which you come back from 1013.25 to QNH. Between them sits the transition layer, usually at least 1000 ft deep. Two rules lock the geometry: the transition level is always higher than the transition altitude, by 1000 ft or more.
Why bother? Because the whole point of the layer is terrain. QNH keeps you honest about the ground; standard setting keeps you honest about each other. The layer is where the handover happens without ambiguity in either direction.
The out-in-the-bush rule
A detail from the notebook that catches people: in VMC, flights intending to land at a point more than 25 nm from any aerodrome with a published transition altitude must observe a height of 2000 ft as a transition altitude. No published number nearby? The default is 2000 ft. Same figure, incidentally, as the height for joining an unmanned airfield — 2000 ft AGL.
Who flies at which level
Once you're on 1013.25, the semicircular rule allocates the levels. From the notes' worked examples: heading 090° puts you on the odd-plus-500 VFR levels —
HDG 090° (odds) → FL035 · 055 · 075 · 095
HDG 205° (evens) → FL025 · 045 · 065 · 085
Eastbound odd, westbound even, VFR riding 500 ft above the IFR levels. And it's possible to be assigned a non-standard level for the semicircular rule — ATC's airspace, ATC's prerogative. Higher up, between FL290 and FL410, RVSM (Reduced Vertical Separation Minima) keeps aircraft just 1000 ft apart — which is why non-RVSM-approved traffic gets planned around that band entirely.