Add up every gain and loss between an access point and a client to find the signal each end receives, how much margin is left, and whether the link is balanced in both directions.
A power budget (or link budget) adds up everything between the two radios: the power one end transmits, the gains of both antennas, and every loss along the way. The result is the signal the other end receives. Comparing that with the signal it needs gives the margin, the headroom left for things that change, such as people, doors and interference.
Wi-Fi is two-way: every frame from the AP is answered by an acknowledgement from the client, and the client sends its own data too. APs often transmit much more power than phones and laptops, so the AP's signal may reach a client that can't be heard back. A client that shows full bars but performs badly is often suffering from exactly this imbalance. Antenna gain helps both directions equally; transmit power only helps the side that sends it.
Path loss here is free space path loss, the loss with nothing in the way (see the Free Space Path Loss tool). Walls and other obstacles add to it: very roughly 3–5 dB for plasterboard, 10–15 dB for a brick wall and 15–25 dB or more for concrete, with more loss at higher frequencies. Real values vary widely, so measure where you can.
−67 dBm is a widely used design target for voice and video, and −70 dBm for general data. The 802.11 standard requires a receiver to decode the lowest rate (MCS 0 at 20 MHz) at −82 dBm, but that gives the slowest speed with no headroom. Faster rates need stronger signals and a quieter background: see the Wi-Fi Modulation Simulator. To convert between dBm and milliwatts, use the mW to dBm Calculator.
Noise, interference and reflections aren't modelled, and neither are MIMO or beamforming gains. Local regulations also cap the EIRP an AP may use, so check the limit for your country and band before raising transmit power or antenna gain.