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I don't understand, even after reading the Wikipedia page, what exactly a "Laplace Transform" is. Apparently it is related to differential equations. It also doesn't seem to be a verb, but rather a characteristic of functions?

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    It is a type of integral transform: https://en.wikipedia.org/wiki/Integral_transform – 2017-01-05
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    When you plug $y(t) = e^{-st}$ into an ordinary differential equation, nice things happen and you get a [polynomial equation](https://en.wikipedia.org/wiki/Characteristic_equation_(calculus)). The Laplace transform exploits this and is a linear operator transforming the function to the "Laplace/Fourier domain", the inverse Fourier/Laplace transform allowing us to write $y(t) = \frac{1}{2\pi}\int_{\infty}^\infty Y(a+i \omega) e^{-(a+i\omega)t}dt$ which means $y(t)$ is a sum (integral) of exponentials. – 2017-01-05
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    @user1952009 yesterday we learned how to solve dy/dx = 5y. i have a LONG way to go – 2017-01-05

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Well this question is fairly broad but hopefully I can provide some insight. So the Laplace transform of a function $f(t)$ is denoted by $\mathcal{L}(f(t))$ is used in differential equations to transform it into something more algebraic. In your standard ordinary differential equations you will learn the Laplace transform and is useful in electrical engineering (so I'm told someone can correct me later). Yeah check the Wikipedia in the comments but in general $\mathcal{L}(f(t))=\int_{0}^{\infty}e^{-st}f(t)\text{d}t$ this supposedly comes from Fourier series something else that you should look up.