echt
real
Authentic, original, and not fake or imitation.
Diese Handtasche ist aus echtem Leder.
This handbag is made of real leather.

real / really
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real
Authentic, original, and not fake or imitation.
Diese Handtasche ist aus echtem Leder.
This handbag is made of real leather.

'Echt' can stand before a noun as an adjective and is then declined. But it can also stand as an unchanging adverb for emphasis before an adjective or verb.
Das ist ein echtes Problem.
That is a real problem.
In the meaning 'authentisch' (authentic), 'echt' is often used to describe materials. Common combinations are 'echtes Gold' (real gold), 'echtes Leder' (real leather), or 'echte Perlen' (real pearls).
Er trägt einen Ring aus echtem Gold.
He is wearing a ring made of real gold.
The use of 'echt' as an adverb for emphasis (in the sense of 'wirklich' (really) or 'sehr' (very)) is typical of colloquial speech. It should be avoided in formal or written contexts.
Ich bin echt müde heute.
I'm really tired today.
To express sincerity, 'echt' is often combined with feelings or social relationships. Typical examples are 'echte Freude' (genuine joy), 'echtes Interesse' (genuine interest), or 'ein echter Freund' (a true friend).
Sie ist eine echte Freundin, auf die ich mich immer verlassen kann.
She is a true friend whom I can always rely on.
very
'sehr' and 'echt' can both intensify something. In this use, 'echt' means roughly 'very' or 'really'. The most important difference is style: 'sehr' fits almost all situations and sounds neutral. 'echt' is colloquial and is more suitable in conversations with friends, family, or colleagues. In formal texts or polite situations, 'sehr' is usually more natural.

Der Kuchen ist echt lecker, weil er so frisch schmeckt.
The cake is really delicious because it tastes so fresh.
Heute ist der kleine Laden in der Nachbarschaft sehr voll.
Today the small shop in the neighborhood is very crowded.