Arrays aren't flexible - they can't increase and decrease in size once they are declared.
What I would do is replace the array with a List, but even if we do that you need to look fairly carefully at what exactly you are trying to do - that code is decidedly odd.
foreach (var synonym in meaning.Synonyms)
{
synonym1 = meaning.Synonyms.ToList();
}
Why do you have a loop here at all, given it just does the same thing every time you go round it?
Probably what you want to do is something like this:
List<string> synonyms = new List<string>();
foreach (ThesMeaning meaning in tr.Meanings)
{
synonyms.AddRange(meaning.Synonyms);
}
Console.WriteLine(string.Join("\n", synonyms.ToArray()));</string></string>