While moving / placing a component, there are three component pushing modes. The current mode can be set through: Preferences ► PCB Editor ► Interactive Routing ► Dragging ► Component Pushing.
You can also switch between the modes while directly on the PCB by pressing the key "R" while dragging the component as described here:
Press the R key to cycle through component push modes. The following modes are supported:
Ignore - default behavior, where the component can be moved regardless of creating a violation with neighboring component(s). In this mode, the same component clearance checking routines seen in previous versions of Altium Designer are used. These routines use the 3D body (if there is one) or the copper and silk primitives to identify an object's clearance.
Push - the component will push other components away to provide compliance with clearances between components. Components in unions can be pushed and the location of components in the union may change, but the union will not break. Locked components can not be pushed. In this mode, components are identified by their selection boundary, which is the smallest possible rectangle that encloses all of the primitives in the component.
Avoid - the component will be forced to avoid violating clearance rules between other components. In this mode, components are identified by their selection boundary, which is the smallest possible rectangle that encloses all of the primitives in the component. (https://www.altium.com/documentation/altium-designer/pcb-cmd-moveobjectmoveobject-ad)
Which mode is currently active is visible in the status bar of Altium Designer: