In the examples you cited, both the quotes and the italics are being used for emphasis-- they're drawing attention to a specific term that you want the reader to distinguish. In that case, both are fairly interchangeable, though each will read better in a different situation.
Italics are generally used for emphasis, or to draw attention to a special term e.g. the title of a book, a foreign language word used in English, and in dialogue, a word or phrase that is spoken forcefully. Quotes are used to, well, quote what someone said, or to draw attention to a specific word, normally one whose usage might be a little odd in that scenario or may not be familiar to the reader.
In the case you cited, I would actually recommend single quotation marks:
Yesterday, I saw an interesting type of flower called an 'eggplant'.
The word 'apple' is a noun.
Since double quotation marks are more often reserved for dialogue or a direct quotation. In the first case, the reason you're using the quotes is because you're assuming the reader may not be familiar with the term 'eggplant'. Be careful with this, as it can look a little silly to put quotations around a term that's actually well-known:
I found out about this cool thing called the 'Internet'.
Think of Dr. Evil and his 'laser' beam. Anyway, in the second example, you're using quotes to ensure that the reader knows you're referring to the word 'apple' alone. It's a helpful convention for explaining or describing things. It can avoid confusion, like in the following example:
The password is apple backwards.
The password is 'apple' backwards.
The first phrase is ambiguous; the reader might think that the password is actually 'apple backwards'. But in the second case, it's clear that the password is 'elppa'.