Learn Danish: Tigeren er en meget stor kat. - The tiger is a very big cat.

Adjectives must agree with the noun they describe. Because kat is a common gender noun (an en word) and the phrase is singular and indefinite (en meget stor kat), the adjective takes its basic, unchanged form: stor. If it were a neuter noun (an et word), it would be stort, and if the phrase were definite or plural, it would be store.

I learned that meget means "much" or "a lot". How does it mean "very" in this sentence?

In Danish, meget is a very versatile word. When it stands alone or describes a verb, it means "much" or "a lot". However, when it is placed directly in front of an adjective, like stor in this sentence, it acts as an adverb that translates to "very".

Because tiger ends in -er, does it change spelling when adding the definite ending to make tigeren?

For the singular definite form shown here, it simply adds -en to the base word to become tigeren. However, you are right to be careful with nouns ending in -er! When you make this word plural, it drops the e and becomes tigre (tigers), and the plural definite form is tigrene (the tigers).