People classify English, German and Dutch into Germanic language group and French, Spanish, Italian into the Romance language family. I learned English and the others before, but I still don't understand why they classify this way, because of the differences of sentence, grammar, structure or their culture in history?
The main difference between the Germanic languages and the Latin (and Celtic) languages is Grimm's Law, which describes a set of sound changes that map Germanic words to their Latin and Celtic cognates. The Germanic sounds were shifted from their Proto-Centum or Proto-Indo-European forms, while the Latin and Celtic sounds either did not change or were changed in some other way (out of scope of this answer).
For example, Germanic th corresponds to Latin t, and Germanic t corresponds to Latin d, so
English tooth corresponds to Spanish diente.
English three corresponds to French trois.
Germanic h corresponds to Latin c, so
German hund and English hound correspond to Classical Latin canis.
German hunnert and English hundred correspond to Classical Latin centum.
Germanic f corresponds to Latin p, so,
English fish corresponds to Spanish pez.
English foot corresponds to French pied (also includes the t - d difference mentioned earlier!).
English father corresponds to Classical Latin pater (also includes the th - t mentioned earlier!).
Some Germanic languages, for example German and Swedish (but not English or Icelandic), have undergone an additional th to d shift. High German has undergone even more. C.f. the High German Sound Shift.
This law is very useful for learning a language in one of the families if you already know a language in the other family. For example, if you know English, you can more easily learn Spanish vocabulary by noting the correspondences.
You can even use this law to map fancy Latin-derived terms in English to their common Germanic forms in English. For example, a "cardiac" arrest can be interpreted as a "heartiac" arrest (using c -> h and d -> t), which is what it is.