Given a set $\Omega$ and a filtration $(\mathcal{F_t}, t\in T)$ on $\Omega$, where $T\subseteq\mathbb{R}$, we say that such a filtration is right-continuous if for every $t\in T$ it holds that $\mathcal{F_t}=\bigcap\limits_{\varepsilon>0}\mathcal{F_{t+\varepsilon}}$.
I was wondering: what is the actual meaning of this property? What is the main intuition behind this definition?