The formation of quasicondensate droplets in ultracold atomic gases is investigated as a first-order phase transition. Physical parameters and size distribution of metastable condensate droplets are derived from conditions of local equilibrium between quasicondensate and normal gas phases. Droplet characteristics are used for the quantitative description of recent measurements of enormous frequency shifts in the $1S\ensuremath{-}2S$ two-photon absorption in spin-polarized hydrogen in the normal gas phase. Theoretical evaluation of the line shape is in good agreement with experimental data.