How capabilities work in Linux is documented in
man 7 capabilities.
Process' capabilities in the effective set are against which permission checks are done. File capabilities are used during execv call (which happens when you want to run another program1) to calculate the new capability sets for the process.
Files have two sets for capabilities, permitted and inheritable and effective bit.
Processes have three capability sets: effective, permitted and inheritable. There is also a bounding set, which limits which capabilities may be added later to process' inherited set and affects how capabilities are calculated during execv. Capabilities can only be dropped from bounding set, not added.
Permissions checks for process are checked against process' effective set. Process can raise its capabilities from permitted to effective set (using capget and capset syscalls, recommended API is respectively cap_get_proc and cap_set_proc).
Inheritable and bounding sets and file capabilities come into play during execv syscall. During execv new effective and permitted sets are calculated and inherited set and bounding set stay unchanged. The algorithm is described in
capabilities man page:
P'(permitted) = (P(inheritable) & F(inheritable)) |
(F(permitted) & cap_bset)
P'(effective) = F(effective) ? P'(permitted) : 0
P'(inheritable) = P(inheritable) [i.e., unchanged]
Where P is old capability set, P' is capability set after execv and F is file capability set.
If a capability is in both process' inheritable set and file's inheritable set (intersection/logical AND) it is added to permitted set. File permitted set is added (union/logical OR) to it (if it is within bounding set).
If effective bit in file capabilities is set, all permitted capabilities are raised to effective after execv.
Capabilities in kernel are actually set for threads, but regarding file capabilities this distinction is usually relevant only if the process alters its own capabilities.
In your example capabilities
cap_dac_override are added to inherited and permitted sets and effective bit is set. When your binary is executed, the process will have those capabilities in effective and permitted sets if they are not limited by a bounding set.
 For fork syscall, all the capabilities and the bounding set are copied from parent process. Changes in uid also have their own semantics how capabilities are set in effective and permitted sets.