The letter ě is a vestige of Old-Czech palatalization. The originally palatalizing phoneme /ě/ [ʲɛ] became extinct, changing to [ɛ] or [jɛ], but it is preserved as a grapheme.
This letter never appears in the initial position, and its pronunciation depends on the preceding consonant:
Dě, tě, ně[ɟɛ, cɛ, ɲɛ] is written instead of ďe, ťe, ňe (analogously to di, ti, ni).
Bě, pě, vě, fě is written instead of bje, pje, vje, fje. But in some words (vjezd, entry, drive-in, objem, volume), bje, vje is written because –je- is part of the etymological root of the word, preceded by the prefix v- or ob-.
Mě[mɲɛ] is written instead of mňe. For etymological reasons, mně is written in some words (jemný, soft -> jemně, softly).
The grapheme is sometimes used in Croatian to denote a jat (něsam', věra, lěpo, pověst, tělo) and is pronounced in different ways depending on the dialect: Ekavian (nesam, vera, lepo, povest, telo), Ikavian (nisam, vira, lipo, povist, tilo) or Jekavian (nijesam, vjera, lijepo, povijest, tijelo). Historically its use was very widespread, but today it is only found in scientific and historically accurate literature.