There are a handful of translations for the word 'yoga', but many, many more interpretations. Yoga as a tradition is a vast body of work that spans many cultures and thousands of years, so it is impossible to narrow it down to one singular definition.
Some of the widely accepted definitions to date are;
Yoga - to 'yoke' or bring together
Yoga - union
Yoga - integration
Yoga - god consciousness
Yoga - skill in action
Yoga - steadying the mind
And there are many more, plus the assumed definition most of us have that Yoga is a 60-75 minute class that involves stretching, breathing and going upside down. This one is not wrong, but it's only half of it. Yoga is both a state of being and a method, so the poses you are doing in that class form part of the method, which ultimately lead you to a state of 'yoga'.
Then what is the state of yoga? What does it describe? What does it mean? Well, to greatly simplify, there are two ways of looking at it. One is that it is the result of union or joining together of matter and consciousness, or rather a recognition of one's inherent wholeness. The former of these two is detailed in the Yoga Sutra of Patanjali, which is a book of aphorisms laid out by Sage Patanjali dating back to 200CE. In this book, Patanjali lays out two fundamentals: Purusha and Prakriti. Purusha is the oneness, the totality, pure consciousness, whilst Prakriti is everything else; nature, matter, imperfection that ultimately amounts to nothing more than an illusion, according to this school of thinking. In the Sutra, Patanjali suggest numerous ways and paths for the yogi to liberate themselves from the illusion, to come back to wholeness (Purusha). This text therefore, if I understand it correctly, is actually more about letting something go to become whole, rather than bringing it all together.
As for Yoga as a state of recognition of inherent wholeness, we first see a suggestion of that going back in time to 300BCE, in the Katha Upanishad. The Upanishads were a series of teachings collected and recorded later as books. These were initially passed down as oral tradition for many many years, and the name 'Upanishad' means 'to sit down near (knowledge/a teacher). In this specific Upanishad, 'yoga' is described as a state of realising God within oneself. Mention of God can be weighted for many, but this is not describing a specific god tied to a specific religion, but rather a totality, not unlike Purusha.
One more prolific definition is 'Yoga is skill in action', a definition that comes from the Bhagavad Gita 200CE, which is a part of the Hindu epic The Mahabharata. The setting for the Gita is a battlefield, not quite the image we are used to when thinking of yoga. You might think the expression 'skill in action' has something to do with physical yoga, but it doesn't in this case, though it is often relayed that way in modern yoga environments. The skill being described here is actually referring to a steady state of consciousness, no matter the battles we face, whether those be actual battles, or battles within ourselves.
Yoga didn't come close to describing something we should do with our body until around 900 CE, with the flourishing of Hatha Yoga when the body began to be incorporated into the pursuit of union and liberation. Why were people using the body for this? One reason may have been that, alongside the proliferation of Hatha Yoga ran a new fascination with science of alchemy, leading to a curiosity about the nature of the matter of the body and how it could be shifted. Tantra yogis explored this and some even believed that dedicated practice could lead one to attain supernatural powers.
If we fast forward to today, the yoga we practice seems to be almost entirely physical, with some of us knowing little fragments of philosophical thought, but not being able to integrate the two. We can fall into the trap of ignoring all the aspects other than the physical, which ends up appropriative, or overdoing those elements and exoticizing the practice of yoga.
In reality, it is much simpler than that. Yoga is very simple in its essence, we just tend to make it complicated. If you look at all of the definitions of yoga as a 'state' of being, they all more or less bring you to the same answer; it is essentially already there. The state of union, integration, wholeness, whatever word works for you, is already within. We practice yoga to realise it.
So, how does this translate into your practice? Start with the breath. Notice each breath cycle and notice the perfect way in which your body intelligently breaths for you. Sit with this for a while until you start to notice the spaces between the breaths. Notice your thoughts, sit with them for a while until you start to notice those glimpses of nothingness in between each thought. When practising poses, catch yourself in that brief yet perfect midpoint between push and pull, between effort and ease. That's your yoga.