Health Crates are located in the background of the combat sequences in Lara Croft: Relic Run. For example in the Jungle Temple level one has to shoot them while simultaneously fighting off the Lizard Men. As the lizards are also throwing their spears back at Lara, this can be quite tricky. When Lara shoots one of these crates her health increases as indicated by the Health Bar.
In addition to health crates there are also Coin Crates located throughout these sequences, which contain coins, the in-game currency used to upgrade Lara, and Ammo Crates, which contain Ammo for the Secondary Weapon.