Limiting magnitude is used to evaluate the quality of observing conditions. It tells the magnitude of the faintest star visible to the unaided eye. The limiting magnitude could also be observed by some instrument. It describes well the sky's transparency: better transparency means that fainter stars are visible.
Limiting magnitude is used eg. in meteor and deep sky observations. It can be used also to approximate light pollution.
The simplest way to evaluate limiting magnitude is to find suitable stars with known magnitudes from star map and check which of them are visible. A more clever way is to count visible stars inside known star squares and triangles. This method was originally invented by meteor observers.
Area Corner stars Constellation 1 Chi-Zeta-Delta-Xi Dra Draco 2 Beta-Delta-Zeta Per Perseus 3 23-Theta-Beta UMa Ursa Major 4 Alpha-Epsilon-Beta Gem Gemini 5 Zeta-Gamma-Delta Aql Aquila 6 Alpha And--Gamma-Alpha Peg Pegasus-Andromeda 7 Alpha-Beta-Delta Cep Cepheus 8 Alpha-Beta-Zeta Tau Taurus 9 Alpha-Beta-Gamma-Delta Leo Leo 10 Alpha-Zeta-Gamma Vir Virgo 11 Alpha CrB--Gamma-Alpha Boo Corona Borealis-Bootes 12 Alpha Ser--Beta Lib--Delta Oph Serpens-Libra-Ophiuchus 13 Beta-Zeta Lyr--Theta-Nu Her Lyra-Hercules 14 Epsilon-Eta-Gamma Cyg Cygnus 15 Beta Dra--Tau-Pi Her Draco-Hercules 16 Alpha CVn--Epsilon-Eta UMa Canes Venatici-Ursa Major 17 Epsilon-Theta-Delta Aur Auriga 18 Mu-Gamma-Phi And Andromeda 19 Kappa-Alpha Dra--Beta UMi Draco-Ursa Minor 20 42-Beta-Gamma Cam Camelopardalis 21 Alpha PsA--98-Delta Aqr Pisces Austrinus-Aquarius 22 Beta Lep--Beta Ori--53 Eri Lepus-Orion-Eridanus 23 Delta-Gamma-Epsilon-Beta Crv Corvus 24 Beta-Gamma-Sigma-Alpha Lib Libra 25 Alpha-Epsilon Sco--Chi Lup Scorpius-Lupus 26 Gamma-Alpha TrA--Eta Ara--Alpha Cen Triangulum Astrinus-Ara-Centaurus 27 Beta Cen-Alpha-Gamma Cru Centaurus-Crux 28 Beta-Epsilon-Iota Car Carina 29 Gamma-Alpha-Beta Hyd Hydrus 30 Alpha Tuc--Alpha-Epsilon Pav Tucana-Pavo
Another version of this information (with nice black-on-white star charts) is available at the IMO Major-Shower Observations page.