Team Fortress 2, being based on the Source Engine, is generally configured to make use of lag compensation. Lag compensation is most commonly the technical reason behind cases of kills or actions that would otherwise seem infeasible in given circumstances; for example, when players perceive themselves to have been "shot through a wall" by a Sniper, backstabs being performed at the incorrect angle (known as facestabs), or otherwise missing entirely (known as failstabs).
When a high-latency (high-ping) player attacks, the server temporarily "rewinds" its copy of the action in order to compensate for their lag. For example, the enemy Sniper shoots when he sees your head, at that moment you and most other players may believe you successfully ran behind a wall. When the server receives the fire message from the Sniper, it "rewinds", finds out if you had ought to have been hit, and then deals damage, leading to the appearance of being "killed through a wall".
This is an intentional engineering and design decision, a tradeoff to enhance the realism of attacks at the expense of the realism of taking damage. Were lag compensation disabled, many players would complain that they shot the enemy without inflicting any damage, which is still a issue due to hit registry and which is more of a issue with melee weapons.
Projectile weapons such as rockets, grenades, syringes, and flares are not lag-compensated. The Pyro's compression blast and Flamethrower are also not lag compensated, despite the effects appearing immediately after firing on a player's screen. This makes Pyro an increasingly difficult class to play at higher latencies.
Spectators do not have lag compensation. If you are spectating someone in first person, you are not seeing exactly what they are seeing, rather you are looking at what the server is seeing. This is especially noticeable with high-latency Snipers, where you should expect to see unusual shots that may appear to miss or jerk about from your perspective.
See the following links for in-depth technical explanation of how lag compensation works in the Source Engine: