Alistair Croll and Benjamin Yoskovitz (1) define a "good metric" as "a number that drives the changes you are looking for." Good metrics are:

1. Comparative, not absolute, preferably a ratio or a rate.

2. Simple and easy to remember.

3. Tied to the desired behavior to achieve a goal. Actionable, not vanity.   

Lagging metrics capture what happened, but leading metrics are most valuable because they predict what is going to happen. For example, metrics collected from employee exit interviews are lagging, while metrics from team health checks predictive future attrition. Another example is customer churn (lagging) vs. the rate of complaints (leading).

A pair of correlated metrics help predict the future, but causal metrics also help change it. Many growth hacks take advantage of human psychology. For example, people who sign up for a social media site are more likely to invite friends right at that moment. So an increase in the activation rate causes an increase in the referral rate.   

The term "KPIs" should not be overused to remain "key." Each industry analyst on Wall Street can name a handful of KPIs for the industry s/he follows. For example, for hospitality, it is the trend in the number of nights booked. For gold mining, it is the all-in sustaining costs per ounce compared to the market price of gold. Croll and Yoskovitz use the term "KPIs" in this sense.

In most literature, metrics support KPIs. KPIs support strategic business objectives. Many metrics are meaningless by themselves ("vanity metrics") but are required to support KPI. For example, time on site may be a vanity metric. Still, it supports a KPI of percent of active users, which in turn helps a strategic business objective of increasing user engagement. Croll and Yoskovitz do not use the term "KPIs" in this sense; instead, they prefer "good metric."  

Picking a single most important KPI for the current PDLC phase (or growth engine) creates focus. It is confusing that such KPI is called "one metric that matters" (OMTM).